Tropical Combinatorics
Tropical Combinatorics
Tropical Combinatorics
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tropical semi-ring: (R ∪ {+∞}, ⊕, ⊙) where<br />
x ⊕ y := min(x, y) and x ⊙ y := x + y<br />
<strong>Tropical</strong> Arithmetic<br />
Example<br />
(3 ⊕ 5) ⊙ 2 = 3 + 2 = 5 = min(5, 7) = (3 ⊙ 2) ⊕ (5 ⊙ 2)<br />
History<br />
can be traced back (at least) to the 1960s<br />
e.g., see monography [Cunningham-Green 1979]<br />
optimization, functional analysis, signal processing, . . .<br />
recent development (since 2002) initiated by Kapranov,<br />
Mikhalkin, Sturmfels, . . .